for a rational function f(x)=8/x+2, if the function is factored such that we assume the denominator so as to acquire roots, it will be f(x)=2(4/x+2).

for vertical asymptotes we consider the behavior of the graph by checking by inspection the multiplicity of the factored form i.e., whether even or odd. asymptotic in same direction if multiplicity is even and asymtotic in different direction if the multiplicity is odd.

For this case multiplicity is even implying the curve will go up and down the vertical axis but will not cross it.